The present invention relates generally to wireless communications, and more particularly, to a memory-less Gaussian interference channel (GIC) where K single-antenna users communicate with their respective receivers using Gaussian codebooks and specified power levels.
We consider a memory-less Gaussian interference channel (GIC) where K single-antenna users communicate with their respective receivers using Gaussian codebooks and specified power levels. The broadcast nature of the wireless channel ensures that each receiver receives the transmissions from all users. Each receiver employs a successive group decoder (SGD) with a specified complexity constraint, to decode its designated user. It is aware of the coding schemes employed by some or all other users and may choose to decode some or all of them only if it deems that doing so will aid the decoding of its desired user.
The Gaussian interference channel noted above presents the following problems:    1. Suppose the K users transmit at pre-determined rates. What is the optimal successive group decoder (which meets the complexity constraint) that should be employed at each receiver?    2. Next, suppose the K users are divided into two classes: the class of variable-rate users which demand as much rate as possible above their minimum acceptable rates and the class of fixed-rate users who only desire a constant rate. Then:            2.1 Given the priorities of all variable-rate users, devise a sequential rate allocation scheme that yields a rate-vector that meets the minimum rate requirements of all users and is strongly pareto-optimal over the variable-rate users, i.e., the rate vector is such that the rate assigned to any variable-rate user can be increased only by decreasing the rate assigned to a variable-rate user with higher priority.        2.2 Suppose all variable-rate users have the same priority. Devise a rate allocation scheme that yields a rate-vector that meets the minimum rate requirements of all users and is symmetric-fair over variable-rate users, i.e., each variable-rate user is assigned identical excess rate over its minimum rate requirement and no other such rate allocation can assign a higher rate to any variable-rate user.        2.3 Suppose all variable-rate users have the same priority. Devise a rate allocation scheme that yields a rate-vector that meets the minimum rate requirements of all users and is max-min fair over variable-rate users, i.e., the rate allocation maximizes the smallest excess rate assigned to a variable-rate user over all possible rate allocations that meet the minimum rate requirements of all users.        
There is also a generalized cognitive radio set-up where the K users are divided into two sets: the set of primary users and the set of secondary users. It can be assumed that the transmission rates of the primary users have been determined and each primary user is decodable at its primary receiver. The problems to be addressed are twofold. The first one is to design a method to pick an “active” set of secondary users and the second one is to perform rate allocation for the active set of secondary users. The constraints are that each primary user must achieve its pre-determined rate and no primary receiver will decode any secondary user.
Some special cases of the problems listed above have been attempted before by others. The discussion by A. Motohari and A. K. Khandani, “M-user Gaussian Interference Channles: To Decode the Interference or To Consider it as Noise,” IEEE ISIT, June, 2007, considers a K user GIC where each user transmits at a fixed power and uses a single Gaussian codebook. However, their set-up assumes no complexity constraints on any receiver. The problem of maximizing the desired user's rate at a particular receiver is solved. Note that maximizing only the desired user's rate at a particular receiver may make other users un-decodable at their designated receivers. A sequential rate allocation algorithm is proposed for the case when there are no minimum rate constraints. Finally, an iterative parallel rate allocation algorithm is also provided but it is not monotonic and the rate-vectors obtained prior to convergence need not be decodable.
Another attempt, discussed by M. A. Maddah-Ali, Mahdavi-Doost and A. K. Khandani, “Optimal Order of Decoding for Max-Min Fairness in K-User Memory-less Interference Channels,” IEEE ISIT, June, 2007, considers a K user GIC where each user transmits at a fixed power and uses a single codebook. Each receiver employs the SIC decoder (which is a particular type of SGD). A max-min fair parallel rate-algorithm is designed for the case where there are no minimum rate constraints and only one iteration is allowed.
Accordingly, for the K-User Gaussian situation discussed herein, there is a need for developing solutions which consider the success group decoder (SGD) at each receiver and which addresses the above problems.